Math 192   Calculus 2

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Preview of Chapter 6
A student completing this chapter successfully will be able to:
bulletGraph regions bounded by curves and use the definite integral to find exact area.
bulletRevolve regions about an axis and use the definite integral to find exact volume by methods of disks and shells.
bulletUse the definite integral to find the work done in spring, pumping and cable problems.
bulletDemonstrate the Mean Value Theorem for Integrals.

6.1        6.2        6.3        6.4        6.5

Calculus 2        Lesson 6.1       Area between Curves
The following topics are the most important. Typical exercises from Calculus, 7th edition Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.

 

  
For each region, graph the functions and determine
a. whether the area approximation is basically vertical rectangles P427#1,5,7,9,13,15,23
b. whether the area approximation is basically horizontal rectangles P427 #3,11,17,19
c. the area using the Midpoint Rule P428#43,45,47
Before we can do our first Maple Assignment, we must install Maple and associate the worksheets with the software.

Maple Assignment:  See Maple Assignment

When you are satisfied with your first Maple assignment, you'll need some information on Submitting Maple Assignments for a Grade.

 

Calculus 2        Lesson 6.2      Volume
The following topics are the most important. Typical exercises from Calculus,  7th edition Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1. Define volume. Text
2. Volume found by rotating an object about the x-axis. P438#1,3,7,19,23,27
3. Volume found by rotating an object about the y-axis. P438#5,9,20,24,28
4. Volume found by rotating an object about a line parallel to an axis.  P438#11,13,15,17
5. Volume found with slicing. P439#43,45,47,49,51,53,55
Maple Assignment: none

 

Calculus 2        Lesson 6.3      Volumes by Shells
The following topics are the most important. Typical exercises from Calculus, 7th edition Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1. Give the definition of volume using cylindrical shells. Text
2. Volume found by shells about the y axis. P445#3,5,7
3. Volume found by shells about the x-axis. P445#9,11,13
4. Volume found by shells about a line parallel to an axis. P445#15,17,19
5. Find the volume using any method. P445#37-42
Maple Assignment: See Maple Assignment

Submitting Maple Assignments for a Grade

 

Calculus 2    Lesson 6.4     Work
The following topics are the most important. Typical exercises from Calculus, 7th edition Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1. For Work problems, know the following types:
1.a definition of Force and Work as well as units; Text
1.b. Find work when the force is constant; P449#1,2
1.c Find work when the force varies; P449#3,4,5,6
1.d Find work using Hooke's Law for springs; P450#7,9,11
1.e Find work in cable problems; P450#13,14,15,16
1.f Find work in water problems; P450#17,19,21,23
Maple Assignment: none

 

Calculus 2     Lesson 6.5    Average Value of a Function
The following topics are the most important. Typical exercises from Calculus, 7th edition Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective
1. Find the average value of a function. P453#1,3,5,9,13,17,19
Maple Assignment:  none